Abstract: 

This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for the practical implementation of modern quantum technologies. In studies of open quantum systems per- formed to date, a very common assumption is that the system and the environment are in separated initial states to begin with. One primary objective of this thesis is to critically analyse this assumption. As such, the core of this thesis incorporates the effect of the initial system-environment (SE) correlations that are present in the joint thermal equilibrium state of the system and the environment on the subsequent system dynamics. In this regard, we follow two different approaches to investigate the dynamics. First, we solve an exactly solvable spin-spin model where a central spin system interacts with a collection of quantum spins. We analyse exactly the central spin dynamics, starting from both initially correlated and uncorrelated SE states, and look at the dynamical differences due to the different starting states. Second, we consider an arbitrary system interacting with an arbitrary environment and derive a master equation that describes the system dynamics and also incorporates the effect of the initial SE correlations. This effect of initial correlations is captured by an extra term appearing in the master equation. The master equation is subsequently applied to the paradigmatic SE models such as the spin-boson model and the spin-spin model. We demonstrate that the role played by initial correlations can be noticeable even if the SE coupling strength is kept smaller.

The next part of the thesis deals with estimating the parameters characterizing the environment of a quantum system. After all, in order to predict the dynamics of a quantum system, one needs to know, for example, the cutoff frequency of the environment as well as its temperature. Recently, the use of a single qubit system to infer the characteristics of an environment has attracted considerable interest. We show that the use of two two-level systems can greatly enhance the estimation of the environment parameters. The reason is simple - two two-level systems also get correlated with each other due to their interactions with the environment, and information about the environment is imprinted onto these correlations. We quantitatively demonstrate this by calculating the quantum Fisher information for a two-qubit probe. Finally, in the last part of this thesis, we study the work counting statistics via a Markovian master equation for a periodically driven spin system weakly coupled to its environment of harmonic oscillators.

List of Publications:

Ali Raza Mirza, Muhammad Zia, and Adam Zaman Chaudhry “Master equation incorporating the system-environment correlations present in the joint equilib- rium state” published in Physical Review A, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.042205

Ali Raza Mirza, Mah Noor Jamil, and Adam Zaman Chaudhry “The role of initial system-environment correlations with a spin environment”, https://arxiv.org/abs/2301.07332.

Ali Raza Mirza and Adam Zaman Chaudhry “Improving the estimation of the environment parameters via a two-qubit scheme”, https://arxiv.org/abs/2305.12278.

Ali Raza Mirza and Ahsan Nazir “Work counting statistics in periodically driven strongly coulped quantum systems” (in progress).